Student seminar

Baryon Acoustic Oscillation Kai Wang

6UKPIJWC%GPVGTHQT#UVTQRJ[UKEU  Content

I. Basic facts of cosmology

II. What is Baryon Acoustic Oscillation(BAO)?

III. How to measure BAO?

IV. Alternative method to measure BAO Basic facts of cosmology Level-1: Background Cosmic Pie

Cosmic Thermal History Level-2: Perturbations

Initial condition Matter from inflation

Einstein collisional field Boltzmann equation equation

S. Dodelson, “Modern cosmology” 2008 “Modern cosmology” Dodelson, S. Metric

BAO in photon distribution BAO in matter distribution ) A&A 594, A11 (2016) A&A 594, Planck Collaboration Collaboration Planck M. Tagmark et al. ApJ 606:702–740, (2004 ApJ 606:702–740, al. et Tagmark M. What is Baryonic Acoustic Oscillation(BAO)? Phase-1. baryon coupled with photon

Quantum fluctuations from inflation

Select one Same distribution overdensity peak )

Photon’s pressure push baryon-photon fluid outward Eisenstein, D. J., Seo, H.-J., and White, M. ApJ, 664: 660-674 (2007 664: 660-674 ApJ, M. White, and H.-J., Seo, J., D. Eisenstein, Phase-2. baryon and photon are decoupled

free-streaming photon

leave baryons alone ) Eisenstein, D. J., Seo, H.-J., and White, M. ApJ, 664: 660-674 (2007 664: 660-674 ApJ, M. White, and H.-J., Seo, J., D. Eisenstein, Phase-3. baryon and dark matter attract each other ) Eisenstein, D. J., Seo, H.-J., and White, M. ApJ, 664: 660-674 (2007 664: 660-674 ApJ, M. White, and H.-J., Seo, J., D. Eisenstein,

Next: Nonlinear evolution & Galaxy formation —> another topic

Why we choose BAO to probe our Universe? 1. Large scale —> more linear —> possible to calculate analytically 2. There is a bump —> prominent feature 3. Both radial and tangential information —> better than CMB, which is just a 2D map Where is the ring?

You may need a special eye to help you see the truth.

Or you can use a statistical tool called “Two Point Correlation Function”. How to measure BAO? Step-1. Measure the 2PCF

2PCF:

P12 = [1+ ξ(r)]dV1dV2 Given a galaxy, the probability to find another galaxy with distance r to it.

BAO calculation is linear, but non-linearity enters though… 1. Redshift-Space Distortion(RSD) The peculiar velocity of galaxies will contaminate the conversion from redshift to distance 2. Galaxy bias We use galaxies to trace matter distribution & galaxies are biased tracers 3. Non-linear evolution After forming the BAO peaks, matter will further experience non-linear evolution to form halos and galaxies ……

Reconstruction technique can partly correct these non-linearities… Reconstruction technique

Zel’dovich approximation: Poisson equation: RSD

Displacement field Gravitational potential

Galaxy bias

Give all the galaxies a movement of (to correct matter motion) a movement of (to correct RSD)

original field Matter evolution Real space Redshift space Before recon Before

displacement field reconstructed field Narrower Correct RSD Mon. Not. R. Astron. Soc. 427, 2132–2145 (2012) 2132–2145 427, Soc. Astron. R. Not. Mon. After recon Padmanabhan et al. al. et Padmanabhan Tune the parameters & Draw a banana End the story?

Observation Theory Cosmological parameters Eisenstein, et al. ApJ, 633: 560-574 (2005) 633: 560-574 ApJ, al. et Eisenstein,

Observed 2PCF varies with cosmological parameters! Percival, W. J., Nichol, R. C., Eisenstein, D. J. et al. ApJ, 657: 51-55 (2007) 657: 51-55 ApJ, al. et J. D. Eisenstein, C., R. Nichol, J., W. Percival, Step-2. Deal with the model α : relative position of BAO peak w.r.t. fiducial cosmology

Solution: First, assume a fiducial cosmology Then, use α to tune the position of BAO peak

modeling broad-band shape (like scale-dependent bias, RSD) Mon. Not. R. Astron. Soc. 427, 2146–2167 (2012) 2146–2167 427, Soc. Astron. R. Not. Mon.

fiducial cosmology al. Xu et

Fourier transform the power spectrum

modeling degradation in the BAO peak due to non-linear evolution Results: Padmanabhan et al. 2012 Xu et al. 2012 Eisenstein et al. 2005 Reconstruction & Better model First detection sample: 46,000 LRGs sample: 46,000 LRGs redshift: 0.16 < z < 0.47 redshift: 0.16 < z < 0.47 detection: 4.2σ detection: 3.4σ

SDSS III BOSS 2013 LOWZ + CMASS sample: 100,000 galaxies redshift: 0.2 < z < 0.7 detection: 7σ

SDSS IV eBOSS 2017 sample: 147,000 quasars redshift: 0.8 < z < 2.2 detection: 2.8σ Alternative method to measure BAO Combine galaxies and voids C. Zhao, Y. Liang, C. Tao et al.

1. New technique to find voids 2. Estimator combined galaxies and voids

3. Tune the weight to minimize the variance 4. Better result than just galaxies α σ

w w C. Zhao, “constraining cosmology using large-scale structures” PhD thesis (2017) Conclusion

1. Two levels of cosmology

• Background evolution • Perturbation evolution

2. Three phases of BAO formation

• Photon and baryon coupled • Photon and baryon decoupled • Baryon and dark matter attract each other

3. Two steps to fit the data

• Reconstruct the galaxy distribution • Using a fiducial cosmology, then modeling the broad-band shape and the degradation brought by non-linear evolution Acknowledgements: Thank Yi Mao and Cheng Zhao for helpful advises.